Place the yeast on one side of the bowl and the salt on the other side. Add the sugar and mix through.
With the motor running, add the eggs and milk then knead on medium speed for 10 minutes, until smooth and glossy.
Keep the motor running and gradually add knobs of softened butter until it’s all incorporated and the dough is silky smooth - around 5 minutes.
Put the dough in a clean bowl, cover, and let it rise for 90 minutes, until doubled.
Grease and sugar six 8cm fluted savarin moulds.
When the dough has doubled in size, knock it back and knead it a few times in the bowl. Then place it in a piping bag with large round nozzle and pipe it into the savarin moulds - they should be 2/3 full.
Preheat the oven to 180C.
Leave the dough to to prove for a second time until it almost reaches the top of the moulds.
Bake in the preheated oven for about 15-18 minutes.
Meanwhile, make the syrup by boiling the sugar and rum with 200ml water - allow it to stay at a rolling boil for 2 minutes.
When the babas are cooked - let them cool for a few minutes before very carefully removing from their moulds.
Put them in a dish and pour over half of the syrup. Let them soak it up then turn them over and repeat, before putting them in the fridge to chill.
Whip the cream with icing sugar and vanilla seeds, then put it in a piping bag and chill until needed.
Serve the babas with flavoured cream piped into their centres, and garnish with fruit.
For the hot buttered rum: mix the butter, sugar, maple syrup, salt and spices into a paste.
Add to a cocktail shaker along with the rum, orange peel and finally the boiling water.
Shake to mix, then serve over a cinnamon stick with an orange twist.